Dude...you literally took all your examples from their ONE ALBUM where they were literally a Led Zeppelin clone.
I have to admit I’m giggling because I’m having a tough time believing that people actually believe this. I did some quick math and came to the fair approximation that I have listened to over 85,000 hours of music in my life. Listening to it studiously. I hear almost zero resemblance between VH and Rush beyond the basics I already mentioned. They sound about as much alike as Motley Crue and Primus.
With respect, the "studiously" seems to imply something more objective than just "I like it". I'm calling you on that. I am not saying that they are like Kiss and Aerosmith, but I think there are more similarities than we're admitting here, and I'm getting a whiff of condescension about that. Van Halen is one of the greatest rock bands in history. EVH is as innovative - if not more - than Neal was on drums. These are Mt. Rushmore players. I know the general consensus here is that Neal is one of the greatest lyricists in rock history, but the idea that Roth is simply "yeah, baby, baby, whooo, awww YEAH!" isn't accurate. There is almost always at least one or two songs on each VH album that dig deeper, and I've said many times that "A Different Kind Of Truth" is one of the best - one of my favorite - albums I own LYRICALLY.
These are fundamentally rock trios rooted in the British blues of the late 60's, early 70's. Look at the Feedback EP; THREE Yardbirds tunes (all from the Beck/Page era) and two Who tunes, including Summertime Blues. In the Sammy-era, there were only three covers played: A Apolitical Blues (Little Feat, off OU812), You Really Got Me (The Kinks, the live album) and Won't Get Fooled Again (The Who). Summertime Blues was a frequent cover through the Roth era into the early days of the Hagar era. EVH has widely stated that Clapton is his guy, with Page a close second. (Interestingly, both Lifeson and VH have cited Steve Hackett as an influence; EVH for the tapping, and Lifeson for his acoustic work).
I think the biggest problem here is perception: I don't think I'm saying anything controversial when I say that around these parts, "Van Halen" is considered a bunch of jackasses and "Rush" is considered to be admirable, straight up gentlemen.